M1 June 2005 Q4

EdexcelOld spec8 marksForces & Newton's Laws Resolving Forces

Figure 2: box on a plane inclined at 20 degrees, rope tension 18 N up the slope — Figure 2

A box of mass 2 kg is pulled up a rough plane face by means of a light rope. The plane is inclined at an angle of 20\(^\circ\) to the horizontal, as shown in Figure 2. The rope is parallel to a line of greatest slope of the plane. The tension in the rope is 18 N. The coefficient of friction between the box and the plane is 0.6. By modelling the box as a particle, find

(a) the normal reaction of the plane on the box, (3)

(b) the acceleration of the box. (5)

Scheme	Marks
R (perp to plane): \(R = 2g\cos 20\)	M1 A1
\(\approx 18.4\) or 18 N	A1
	(3)

Scheme	Marks
R (// to plane): \(18 - 2g\sin 20 - F = 2a\)	M1 A1
\(F = 0.6R\) used	B1
Sub and solve: \(a = 0.123\) or 0.12 m s\(^{-2}\)	M1 A1
	(5)
	(8 marks)